Both the Senate Judiciary Committee and the Senate Committee on Commerce, Science, and Transportation have invited Zuckerberg to testify amid the scandal involving the data firm Cambridge Analytica. While the Judiciary Committee originally wanted Zuckerberg to testify alongside Twitter CEO Jack Dorsey and Google CEO Sundar Pichai on April 10, it is now looking to band together with the commerce committee for a joint hearing.

Sen. Dianne Feinstein told reporters at the Silicon Valley Leadership Group in Sunnyvale, California, on Monday that Zuckerberg had agreed to testify. She added in an interview with the San Francisco Chronicle's editorial board that "the question is whether it will be one committee or two."

In addition, a Republican aide told Business Insider the committees were nearing an agreement to host a joint hearing.

A joint hearing would reduce the number of days Zuckerberg would be forced to spend on Capitol Hill, limiting public exposure on what is already shaping up to be bad optics for the social-media giant.

"At the highest level, this is what Congress does best: spank executives in public on behalf of their constituents," said Paul Rosenzweig, a senior fellow at the R Street Institute.

If the two committees follow through and join together for a single hearing — and Zuckerberg accepts — he would still be summoned to Capitol Hill more than once.

The House Committee on Energy and Commerce announced Wednesday that Zuckerberg had accepted its invitation to testify next Wednesday.

"This hearing will be an important opportunity to shed light on critical consumer data privacy issues and help all Americans better understand what happens to their personal information online," said Reps. Greg Walden and Frank Pallone, the committee's top Republican and its top Democrat. "We appreciate Mr. Zuckerberg's willingness to testify before the committee, and we look forward to him answering our questions on April 11th."

Zuckerberg told reporters on Wednesday in a conference call that he would be sending other Facebook officials to brief and testify before governments of other countries such as the United Kingdom.